MATH40004 OLD Practice Paper AUDIT REVISED 2

English passage 1 (6% down the source page) AUDITED_REVISED_2 revision statement

English passage 2 (11% down the source page) The body of this report comes from the previous revised version. Codex's independent review found that the previous main ZIP omitted the 2020 original question booklet and official solutions/marking materials, affecting the 2020 question-level evidence.

English passage 3 (12% down the source page) These question-level claims could not be independently verified within the package.

English passage 4 (15% down the source page) This version includes the original file “MATH40004MATH40011_Calculus and Applications_Q&S;_May_2020(3).pdf” unchanged under 06_SOURCE

English passage 5 (16% down the source page) _EVIDENCE/2020, registered in the original-evidence index and SHA256SUMS. This PDF has 22 pages. Its SHA-256 is:

English passage 6 (19% down the source page) 143a8d4fdaaf7f49f781e464c0794cc7a29cd1f96d25440bc26dafa79164520b Question-level conclusions for 2020–2026 must therefore be read with the original PDFs. Reports cannot replace original materials. Apart from evidence-chain completion and workbook

English passage 7 (22% down the source page) mechanical-format repairs, the report's conclusions have not been recalculated or altered. Version date: 2026-08-06.

English passage 1 (5% down the source page) Old practice questions: retain / modify / replace / retire

English passage 1 (5% down the source page) decision rules

English passage 2 (9% down the source page) A Retain: historically distinct ability and a reliable method. B Modify: correct knowledge, but formulation, combination or difficulty needs adjustment. C Replace: repeated method sequence or label-only coverage. D Retire: beyond scope, incorrect, or unavailable files/conditions. No complete old main question must be permanently retired in this revision, but repeated Airy/Green variants in several old questions are no longer reused as subparts.

English passage 3 (16% down the source page) question-by-question disposition

English passage 4 (20% down the source page) Paper | Question | Disposition | Old content | Rationale P1 | Q1 | B Modify | Integrated Taylor/power-series/improper-integral question, essentially replicating 2026 Q1.

English passage 5 (21% down the source page) Retain the current structural-reinforcement function, allowing only Paper 1 to closely follow 2026; rewrite the function family and error-estimate sequence. P1 Q2 | B Modify | Physical-loss model + Fourier series, replicating 2026 Q2 | The method sequence is valid, but context and combination are excessively anchored; change to a spherical-droplet model and ramp function.

English passage 6 (25% down the source page) P1 | Q3 | B Modify | Complex-eigenvalue system + nonhomogeneous system + integrating factor, replicating 2026 Q3.

English passage 7 (25% down the source page) Retain this combination only as the sole 2026 structural-reinforcement paper; change the matrix, forcing and ODE.

English passage 8 (27% down the source page) P1 | Q4 | B Modify | Bifurcation + Fourier methods for ODEs + implicit-function Taylor, replicating 2026 Q4.

English passage 9 (27% down the source page) Retain the combination only in Paper 1. Several original Airy variations were repetitive and require recalibration.

English passage 10 (29% down the source page) Old question | Disposition | Content | Rationale P2 Q1 | C Replace | Binomial series and improper integrals | Repeats the Q1 method sequence in several papers; change to a 2025 series-test/iteration entry point. P2 Q2 | B Modify | Centroid/geometry + Fourier/Parseval | High historical value, but make the 2025 bridge explicit and reduce fragmentation. P2 Q3 | A Retain | Jordan system + Euler-Cauchy | Directly covers a high-mark 2025 entry point; include after adjusting numbers and marks. P2 Q4 | B Modify | Bifurcation + Fourier transform + Hessian | Three historical families are valid; rearrange as 2025 double bifurcation/Jacobian/Hessian. P3 Q1 | C Replace | Taylor/log/improper integrals | Repeats P1/P4/P6/P8; change to 2023–24 function analysis/Riemann sums/curves. P3 Q2 | A Retain | Centroid + Fourier series | Covers 2022/2024 applications; rework as a 2023–24 geometry/Laplace bridge. P3 Q3 | B Modify | Physical model + Fourier series | Same combination as 2026 Q2; retain methods but distribute across different historical roles. P3 Q4 | C Replace | Bifurcation + Fourier ODE + multivariable Taylor | Typical 2026 anchoring; change to 2023–24 systems/transforms/Euler-Cauchy. P4 Q1 | C Replace | Taylor/improper integrals | High duplication; no extra coverage of earlier definitions/parametric curves. P4 Q2 | C Replace | Application model + Fourier | Still centres on 2026 Q2; change to 2020–22 improper integrals/centroids. P4 Q3 | C Replace | Fourier series + Airy transform | Shifted Airy variants provide label-only coverage without earlier Taylor/sign-function abilities. P4 Q4 | C Replace | Linear system + integrating factor | Repeats 2026 Q3; change to 2020–22 reduction of order/Green/zero-eigenvalue lines/implicit-function error. P5 Q1 | A Retain | Definitions/parametric curves/Riemann sums/convergence | Diverse historical entry points meaningfully add 2020–22 abilities. P5 Q2 | A Retain | Geometric centroid/solid of revolution + differentiated Fourier series | Directly covers earlier geometry and derivative series. P5 Q3 | A Retain | Laplace + nonlinear reduction of order + variation of parameters + system formulation.

English passage 11 (44% down the source page) less common but valuable abilities for rotation across papers .

English passage 12 (46% down the source page) Old question | Disposition | Content | Rationale P5 Q4 | A Retain | Bifurcation + energy theorem + Hessian | Good cross-year mixing; split and redistribute into the revised version. P6 Q1 | C Replace | Log power series/iteration/improper integrals | Duplicates other Q1s; move to the mixed-challenge paper and change the entry point. P6 Q2 | C Replace | Physical model + Fourier | Too many repeated combinations; change to 2022 arc centroid + derivative series. P6 Q3 | C Replace | System + integrating factor | Overlaps P1/P4/P8; change to a centre/resonance and single-variable integrating factor. P6 Q4 | C Replace | Bifurcation + Green function + implicit-function Taylor | Continues copying 2026 Q4; change to nonstandard singularity collision/shifted Airy/second-order spherical Taylor. P7 Q1 | A Retain | Function sketch/integration/parameter series | Fills frequent function-analysis abilities not directly tested in 2026. P7 Q2 | B Modify | 20 marks concentrated on Fourier-transform properties | Valuable knowledge, but excessive concentration distorts time; distribute across bridging/historical papers. P7 Q3 | A Retain | Heaviside ODE + Euler-Cauchy | Directly fills frequent scalar-ODE gaps. P7 Q4 | A Retain | Hessian contours | Fills consistently high-mark 2021–25 abilities; include in the gap paper. P8 Q1 | C Replace | Taylor/iteration/improper integrals | Again replicates 2026 Q1. P8 Q2 | C Replace | Conservation model + Fourier series | Again replicates 2026 Q2. P8 Q3 | C Replace | Jordan system + integrating factor | Again replicates 2026 Q3. P8 Q4 | C Replace | Singularity bifurcation + Green + implicit function | Again replicates 2026 Q4; the original eight-paper compilation is no longer the final training source.

English passage 13 (62% down the source page) summary

English passage 14 (66% down the source page) A Retain: 9 questions; B Modify: 8; C Replace: 15; D Retire complete questions: 0. Old P7/P8 were also audited, but the final set contains only six papers. The old eight-paper compilation is marked retired and excluded from the website import package.